Merkel called the emergency talks after her Bavarian ally, Horst Seehofer of the Christian Social Union (CSU) party, threatened her with unspecified consequences if she did not take action to limit the number of newcomers arriving into Germany by Sunday.
“Several points… still need to be resolved including the issue of 'transit zones',” Merkel's spokesman Steffen Seibert said, referring to a proposal to create airport-style processing points on Germany's borders to allow would-be refugees who do not fulfil asylum criteria to be moved out quickly.
More talks between Merkel, Seehofer and Sigmar Gabriel, leader of the Social Democrats who are in a grand coalition with the CDU/CSU, were planned for Thursday, Seibert said.
The vast majority of the up to one million people expected to arrive in the country this year are crossing the border from Austria into Bavaria.
While most Germans initially backed Merkel's open-doors policy for those fleeing war and persecution, a growing backlash has piled pressure on the chancellor and exposed rifts within her conservative bloc.
The CDU and CSU sought Sunday to paper over their divisions with a joint statement which proposed to suspend for two years the possibility for refugees given “subsidiary protection” — a status that falls short of full asylum – to have family members join them in Germany.
The sister parties also called for a joint German-Austrian police operation on the border to help control the migrant flow.
The document did not broach the thorny issue of the “transit zones”, which the SPD has rejected as too restrictive.
Europe's top economy has taken a range of steps in recent weeks to stem the biggest influx of refugees since the aftermath of World War II.
These include limiting the right to political asylum to exceptional cases for nationals from Albania, Montenegro and Kosovo, and accelerating expulsion procedures for those denied asylum.
On Friday, Germany announced that migrants massing at its border with Austria would now be funnelled through five entry points to foster a more “orderly” passage.
Since the beginning of the year, over 600,000 migrants have landed on Greece's shores, according to the UN refugee agency UNHCR.
Adding arrivals in Italy, the total number of migrants to have crossed the Mediterranean this year stands at over 740,000.